Ty

aliina [53]

To add fractions, find the LCD - lowest common denominater, and then Combine. answer is 8/9. Decimal form = 0.888888..........
For LCD find where both bottom numbers equal the same so in this case you would have to multiply 3 times 3 to equal 9. Once you do that the 2 thats on top of the 3 will also have to be multiplied by 3 so it could make sense. Now you must Combine - it would be 6/9 +2/9. you only add the top numbers and leave the bottom number.(that is what its out of). Thus the answer is 8/9.

Leave a Thank you and a 5 star rate. Thanks ;)

4 0

3 years ago

What is (4-x^2)(4-x^2) ?

Studentka2010 [4]

Answer:

x^4 - 8 x^2 + 16

Step-by-step explanation:

Use formula (a-b)^2 = a^2-2ab+b^2

now a=4 b=x^2, plug in

4 0

3 years ago

C=1/21.22.23+1/22.23.24+................+1/200.201.202 . = là dấu nhân

Aneli [31]

It looks like you have to find the value of the sum,

$C = \displaystyle \frac1{21\times22\times23} + \frac1{22\times23\times24} + \cdots + \frac1{200\times201\times202}$

so that the n-th term in the sum is

$\dfrac1{(21+(n-1))\times(21+n)\times(21+(n+1))} = \dfrac1{(n+20)(n+21)(n+22)}$

for 1 ≤ n ≤ 180.

We can then write the sum as

$\displaystyle C = \sum_{n=1}^{180} \frac1{(n+20)(n+21)(n+22)}$

Break up the summand into partial fractions:

$\dfrac1{(n+20)(n+21)(n+22)} = \dfrac a{n+20} + \dfrac b{n+21} + \dfrac c{n+22}$

Combine the fractions into one with a common denominator and set the numerators equal to one another:

$1 = a(n+21)(n+22) + b(n+20)(n+22) + c(n+20)(n+21)$

Expand the right side and collect terms with the same power of n :

$1 = a(n^2+43n+462)+b(n^2+42n+440) + c(n^2+41n + 420) \\\\ 1 = (a+b+c)n^2 + (43a+42b+41c)n + 462a+440b+420c$

Then

a + b + c = 0

43a + 42b + 41c = 0

462a + 440b + 420c = 1

==> a = 1/2, b = -1, c = 1/2

Now our sum is

$\displaystyle C = \sum_{n=1}^{180} \left(\frac1{2(n+20)}-\frac1{n+21}+\frac1{2(n+22)}\right)$

which is a telescoping sum. If we write out the first and last few terms, we have

C = 1/(2×21) - 1/22 + 1/(2×23)

… … + 1/(2×22) - 1/23 + 1/(2×24)

… … + 1/(2×23) - 1/24 + 1/(2×25)

… … + 1/(2×24) - 1/25 + 1/(2×26)

… … + … - … + …

… … + 1/(2×198) - 1/199 + 1/(2×200)

… … + 1/(2×199) - 1/200 + 1/(2×201)

… … + 1/(2×200) - 1/201 + 1/(2×202)

Notice the diagonal pattern of underlined and bolded terms that add up to zero (e.g. 1/(2×23) - 1/23 + 1/(2×23) = 1/23 - 1/23 = 0). So, like a telescope, the sum collapses down to a simple sum of just six terms,

C = 1/(2×21) - 1/22 + 1/(2×22) + 1/(2×201) - 1/201 + 1/(2×202)

which we simplify further to

C = 1/42 - 1/44 - 1/402 + 1/404

C = 1,115/1,042,118 ≈ 0.00106994

4 0

3 years ago

What is the input value other than 7 for which g(x)=4

Vsevolod [243]

Given:

It is given that the value of the graph when the input 7 is $g(x)=4$

We need to determine the value of x when $g(x)=4$

Value of x when $g(x)=4$ :

The value of x can be determined by using the graph.

From the graph, we need to determine the value of x when $g(x)=4$ other than the value x = 7.

This can be determined by finding the point at which the line meets the point y = 4, we can find the corresponding x - value.

Thus, from the graph, it is obvious that the graph also meets the point y = 4 when x = -8.

Therefore, the input value is x = -8 which makes $g(x)=4$

Hence, the input value other than 7 for which $g(x)=4$ is x = -8.

7 0

3 years ago

I need help with these anyone know

Brilliant_brown [7]

7. 20
8. 680
9. 700
10. 4,000
11. 106,000
12. 5,800

7 0

4 years ago